A circle with centre 'O' has a radius of 39 cm. If the length of cord PQ is 72 cm, then find OA:OP, given that PA:PQ = 1:2 and the points 'P', 'A' and 'Q' are collinear
In right triangle AOP, OP = 39 cm Also, (PA/PQ) = (1/2) Or, (PA/72) = (1/2) So, PA = 36 cm We know that the perpendicular drawn through the circle bisects the chord. So, ∠ PAO = ∠ PAQ = 90o So, OA2 = OP2 - PA2 {Using Pythagoras theorem} Or, OA = √(1521 - 1296) = 15 cm So, required ratio = 15:39 = 5:13
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